First, this man is extremely lucky. Most people under brutal attack die or got into coma.
But I'd like to comment on this line:
Everywhere he looks, he sees complex mathematical formulas -- like the Pythagorean theorem, for example.
Hmm, is the Pythagorean theorem all that complex? Waita minute are you talking about some Pythagorean Theorem involving complex numbers? (I don't think so...) If you look around, just about everything can be drawn by breaking things down into little triangles (and then right triangles) so the Pythagorean Theorem applies everywhere... That's how computer graphics work basically...
A visual representation of π? Here, call up your favorite pizza restaurant. Get a 24 inch pizza (do they sell that big size?) Instantly you get a visual (and edible) representation. That area of the pizza (in square feet) is 1*1*π = π. Order a 12 inch pizza, that circumference is 2*(1/2)*π inches.
A much more fascinating view of π are the infinite equations, such as the Gregory's Formula, and the Viete's Formula, and many more.
Fractals! The mysterious composition of small shapes... Some can be cranked out by a computer by iterations of complex (meaning complex numbers) equations. For instance, the Mandelbrot set is given by this relationship: zn+1 = zn2 + c. Fractals CAN'T really be drawn by hand exactly because there are infinitely small parts. Alas, fractals don't have a lot of practical uses except drawing terrains to simulate some landscape in some video games.
So yes, this lucky man's brain is probably active now so he can perceive things not previously thought before, and creativity is needed in mathematics!
I think he should study some open problems and prove some age-old theorems and contribute to the world with his genius ability. Don't know where to start? try these million dollar problems.
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